1. ## Word problems

This is from a previous years math competition. Matemaattisten Aineiden Opettajien Liitto MAOL ry : Tehtäviä

If an empty bath is plugged and the tap opened, the tub fills in a minutes. if the plug is removed the bath empties in b minutes , b>a. How long will it take for the bath to fill if the tap is opened and the plug taken away?

Can you please also explain how one "begins" to solve a word problem as such?

Thank you!

2. Originally Posted by Coach
This is from a previous years math competition. Matemaattisten Aineiden Opettajien Liitto MAOL ry : Tehtäviä
Ihan totta? Selaisia on hienoa!! Olenhan minä haltioitunut siitä, että saan tietoa siitä. Kiitoksia!

If an empty bath is plugged and the tap opened, the tub fills in a minutes. if the plug is removed the bath empties in b minutes , b>a. How long will it take for the bath to fill if the tap is opened and the plug taken away?
The difficulty in such problems tends to be the nature of the units. Switching around the units make it all more clear.

With the tap opened, it fills in a minutes. Translation: The tap can fill (1/a) bathtubs in one minute.

With the drain opened, it drains in b minutes. Translation: The drain can drain (1/b) bathtubs in one minute.

Since b > a, we have 1/b < 1/a

Working against each other, we manage to fill [(1/a) - (1/b)] bathtubs per minute. How long does it take to fill a whole bathtub at that rate? A little algebra remains.